Support was so widespread that half of self-identified Republicans said they supported a public plan, according to the poll.

President Obama has argued that his health care overhaul would bring down costs for consumers while also expanding coverage. His opponents have warned that expanding government bureaucracy would crowd out private industry and lessen the quality of care.

Despite 77 percent of those polled who said they were "very or somewhat" satisfied with their current plan, 85 percent said the health care system should still be rebuilt from scratch.

“It is the responsibility of the government to guarantee insurance for all,” Juanita Lomaz, a 65-year-old office worker from Bakersfield, Calif. told the Times. “But my care will get worse because they’ll have to limit care in order to cover everyone.”

Sen. Lindsey Graham said Sunday the Senate would not let the U.S. "go down the government-run health care road."

Speaking on ABC’s “This Week,” the South Carolina Republican said Obama's plan would let a government bureaucrat stand between people needing treatment and their doctors.

Sen. Chris Dodd, D-Conn., who heads the reform effort in the Senate, pointed to the latest poll and said Americans want a government role in health care and have expressed a willingness to pay higher taxes for that.